hapantad2j

2022-04-30

Prove:

$\underset{n\Rightarrow \mathrm{\infty}}{lim}\mathrm{ln}\left(\frac{n+1}{n}\right)=0$

Landyn Whitney

Beginner2022-05-01Added 19 answers

Here ${a}_{n}=\mathrm{ln}\left(\frac{n+1}{n}\right)$ and $a=0$

Then, for any given$\xi >0$

Let$|{a}_{n}-a|<\xi$

$|\mathrm{ln}\left(\frac{n+1}{n}\right)-0|<\xi$

$\mathrm{ln}(\frac{n+1}{n}<\xi$

$\frac{n+1}{n}<{e}^{\xi}$

$\frac{n}{n}+\frac{1}{n}<{e}^{\xi}$

$1+\frac{1}{n}<{e}^{\xi}$

$\frac{1}{n}<{e}^{\xi}-1$

Thus, by Archimedian Property$\mathrm{\exists}N\in N$ such that

$\frac{1}{n}<{e}^{\xi}-1$ , $\mathrm{\forall}n\ge N$

Therefore,$\underset{n\Rightarrow \mathrm{\infty}}{lim}{a}_{n}=a$

$\underset{n\Rightarrow \mathrm{\infty}}{lim}\mathrm{ln}\left(\frac{n+1}{n}\right)=0$

Then, for any given

Let

Thus, by Archimedian Property

Therefore,

Find the volume V of the described solid S

A cap of a sphere with radius r and height h.

V=??

Whether each of these functions is a bijection from R to R.

a) $f(x)=-3x+4$

b) $f\left(x\right)=-3{x}^{2}+7$

c) $f(x)=\frac{x+1}{x+2}$

?

$d)f\left(x\right)={x}^{5}+1$In how many different orders can five runners finish a race if no ties are allowed???

State which of the following are linear functions?

a.$f(x)=3$

b.$g(x)=5-2x$

c.$h\left(x\right)=\frac{2}{x}+3$

d.$t(x)=5(x-2)$ Three ounces of cinnamon costs $2.40. If there are 16 ounces in 1 pound, how much does cinnamon cost per pound?

A square is also a

A)Rhombus;

B)Parallelogram;

C)Kite;

D)none of theseWhat is the order of the numbers from least to greatest.

$A=1.5\times {10}^{3}$,

$B=1.4\times {10}^{-1}$,

$C=2\times {10}^{3}$,

$D=1.4\times {10}^{-2}$Write the numerical value of $1.75\times {10}^{-3}$

Solve for y. 2y - 3 = 9

A)5;

B)4;

C)6;

D)3How to graph $y=\frac{1}{2}x-1$?

How to graph $y=2x+1$ using a table?

simplify $\sqrt{257}$

How to find the vertex of the parabola by completing the square ${x}^{2}-6x+8=y$?

There are 60 minutes in an hour. How many minutes are there in a day (24 hours)?

Write 18 thousand in scientific notation.